阅读说明：本技术 一种基于mimo雷达低旁瓣发射方向图设计方法 (One kind being based on MIMO radar low sidelobe transmitting pattern design method ) 是由 窦慧晶 肖子恒 杨帆 谢金鑫 于 2019-07-16 设计创作，主要内容包括：一种基于MIMO雷达低旁瓣发射方向图方法,属于阵列信号处理技术领域。传统最小化旁瓣算法是通过添加主瓣和旁瓣功率约束来实现减低旁瓣和提高主瓣信号功率,进而提高目标检测能力,但是可能造成主瓣分裂,不能对主瓣约束和赋形。针对这一问题,本文提出了基于MIMO雷达改进的最小化旁瓣方法,该方法保留了最小化旁瓣算法的优点,利用主瓣上界和下界对主瓣进行约束,利用半功率点将空间分为主瓣区和旁瓣区,分别以主瓣和峰值旁瓣之差最大值为目标函数,以各阵元发射信号恒定为约束条件,通过改变主瓣上界对主瓣波动的限制,建立半正定规划问题,利用凸优化求得最优解,该方法只利用一次凸优化求解,即可实现低旁瓣可控波形。(One kind being based on MIMO radar low sidelobe direction of the launch drawing method, belongs to array signal processing technology.It is to realize to lower secondary lobe and improve main lobe signal power by addition main lobe and side-lobes power constraint, and then improve target detection capabilities, but may cause main lobe division that tradition, which minimizes secondary lobe algorithm, cannot be to constraint of the main lobe and figuration.For this problem, this paper presents be based on the improved minimum secondary lobe method of MIMO radar, this method remains the advantages of minimizing secondary lobe algorithm, it is constrained using the main lobe upper bound and lower bound pair main lobe, space is divided into main lobe area and secondary lobe area using half power points, respectively using the difference maximum value of main lobe and peak side-lobe as objective function, it is set to constraint condition with each array element transmitting signal constant, by the limitation for changing bound pair main lobe fluctuation on main lobe, establish semi definite programming problem, optimal solution is acquired using convex optimization, this method only utilizes primary convex Optimization Solution, the controllable waveform of low sidelobe can be realized.)

1. one kind is based on MIMO radar low sidelobe transmitting pattern design method, which is characterized in that specific as follows:

Step 1: emulated to MIMO radar transmitting signal, by radar mockup be set as transmitting terminal be made of M array element it is uniform Linear array；Wherein m-th of antenna element transmitting signal is expressed as s_m, then transmitting signal matrix can be indicated are as follows: 1≤m≤M；

S=[s₁,s₂,…,s_M]^T

Assuming that far field objects be located at intended recipient at θ to signal X be

X=a^H(θ)S

Wherein a (θ) indicates that MIMO radar emits signal guide vector, a^H(θ) is the transposition of steering vector a (θ),Carrier frequency is f_c, c represents the light velocity, and array element spacing is d； It can thus be concluded that directional diagram expression formula P (θ) are as follows:

Wherein, L indicates that Baud Length, covariance matrix R are P (θ), and covariance matrix R will direct shadow as can be seen from the above equation Transmitting pattern spatial characteristics are rung, P (θ) directly indicates distribution of the power at corresponding angle θ, obtains transmitting signal mode Type；

Step 2: utilizing Ω_SIndicate secondary lobe region, Ω_mMain lobe region is indicated, with θ₁, θ₂Respectively indicate the left half-power beam of main lobe Point and right half-power beam point, centre folded by region be main lobe Ω_m, the region other than left and right half-power beam point is Ω_S；It can obtain Transmitting pattern θ_sThe side-lobes power expression formula in direction are as follows:

a^H(θ_s)Ra(θ_s),θ_s∈Ω_s

Transmitting pattern θ_m(θ_m∈Ω_m) direction main lobe power expression:

a^H(θ_m)Ra(θ_m),θ_m∈Ω_m

Step 3: set the main lobe upper bound as β and main lobe lower bound be η, η be set as 1, β indicate constraint of the main lobe be it is variable, constraint is such as Under:

η indicates main lobe lower bound, then:

a^H(θ_m)Ra(θ_m)≥η,θ_m∈Ω_m

β is the constraint of the main lobe upper bound, is made:

|a^H(θ_m)Ra(θ_m)-η|≤β,θ_m∈Ω_m

Step 4: θ_m0(θ_m0∈Ω_m) indicate main lobe center power point, the constraint of three dB bandwidth half power points are as follows:

Step 5: might have the radar scattering echo of other objects other than clutter i.e. target in secondary lobe area in actual environment It influences to receive signal, the echo signal-to-noise ratio of MIMO radar is caused to reduce, and then influence MIMO radar and estimate performance；In secondary lobe region Clutter θ_lPlace generates corresponding null to inhibit to strong clutter；If δ > ε > 0, δ are any number greater than 0；If there is miscellaneous The influence of wave, is added in constraint condition: being just added without the following conditions if there is no clutter；

a^H(θ_l)Ra(θ_l)≤ε,θ_l∈Ω_s

Step 6: not influencing MIMO radar detection performance to guarantee that each array element transmission power is equal, enabling R_mmIndicate m-th pair Diagonal element, wherein 0 < m < M；The following constraint of addition:

R_mm=1/M

Step 7: guaranteeing its low sidelobe characteristic, θ using the difference of main lobe center power and peak side-lobe power as objective function_m0 (θ_m0∈Ω_m) indicating main lobe central point, objective function form is as follows:

a^H(θ_m0)Ra(θ_m0)-a^H(θ_s)Ra(θ_s)

Step 8: covariance matrix R >=0 is enabled to guarantee its Positive, using in the 7th step constraint function and step third extremely The constraint condition of 7th step establishes positive semidefinite Optimized model as follows:

Step 9: obtaining Optimized model by the 8th step, is solved, sent out using Matlab convexity Optimization Toolbox cvx Signal covariance matrix is penetrated, and then acquires transmitting signal.

Technical field

It is mainly a kind of to utilize bound pair main lobe under the main lobe upper bound and main lobe the invention belongs to array signal processing technology It is constrained, the difference of increase main lobe center power and peak side-lobe power is realized by increasing dividing value on main lobe, thus establishes half Positive definite planning problem solves the method for realizing low sidelobe characteristic.

Background technique

Multiple-input and multiple-output (MIMO) radar is the new radar mode that scholar proposes on the basis of phased array radar, from proposition When compared to phased array radar have a clear superiority and become hot topic, Centralized Mode and distribution can be divided into according to array element structure difference Formula mode.This paper main research is centralized MIMO radar, and centralized MIMO radar utilizes small array element spacing, improves hair The flexibility of Design of Signal is penetrated, plays the performance advantage of MIMO radar waveform diversity to the greatest extent.In comparison, centralized MIMO radar has higher estimated accuracy when carrying out DOA estimation, so being always for the design of centralized MIMO radar waveform Hot spot in research.

There are orthogonal waveforms design and waveform correlation to design both of which in the Waveform Design of centralized MIMO radar: utilizing Orthogonal waveforms carry out the irradiation in full airspace, find target present in airspace, this mode is mainly used in the target search stage；And It after target occurs, is tracked using relevant waveform, improves detection performance, this mode is mainly used in the target tracking stage；It is right The problem of influencing MIMO radar tracking performance with sidelobe clutter is interfered in the secondary lobe that secondary lobe generates, using in direction of the launch G- Design Middle reduction side-lobe energy improves main lobe energy, improves influence of the secondary lobe to MIMO radar Mutual coupling.Weighting is proposed earliest Method, directional diagram is weighted by introducing weighting matrix, but to will cause MIMO radar power distribution uneven for weighting, influences Radar range；It then proposes the part waveform correlation design method based on semi definite programming, but only considers low sidelobe characteristic, The problems such as ignoring and main lobe regulated and controled, main lobe distortion can be generated.Therefore, set forth herein one kind to be based on MIMO radar low sidelobe launch party To drawing method, this method is objective function using the maximum value of the difference of main lobe center power and side lobe peak power, passes through main lobe Bound pair main lobe addition constraint makes main lobe power to the greatest extent may be used while dividing value on increasing main lobe and reduction secondary lobe under the upper bound and main lobe It can increase the difference of main lobe center power and peak side-lobe power close to the main lobe upper bound, be achieved in the characteristic of low sidelobe.Consider real In a direction, there may be the influences of strong clutter in border, can form null in specific direction and be inhibited.Context of methods purport By reducing transmitting pattern secondary lobe, mitigates sidelobe clutter and secondary lobe interferes the influence generated to MIMO radar, improve DOA and estimate Precision is counted, system block diagram is as shown in Figure 1.

Summary of the invention

The technical problem to be solved by the present invention is to using semi definite programming class algorithm in the same of design low sidelobe directional diagram When, it is constrained by being added to main lobe, realization can reduce secondary lobe while improving main lobe center power, and to strong miscellaneous in space The influence of wave forms null and is inhibited, and thus improves accuracy and stability when MIMO radar carries out DOA estimation.

To solve the above problems, the present invention adopts the following technical scheme that:

One kind minimizing secondary lobe design method based on MIMO radar transmitting pattern, and the particular content of this method is as follows:

The first step emits signal by MIMO radar and is emulated, obtain target received signal, obtains signal power and hair Penetrate the direct relationship of signal covariance matrix.

Second step establishes semi definite programming problem, first according to the relationship of transmitting signal covariance matrix and signal power Using the difference of the maximum power of transmitting signal main lobe power and peak side-lobe as objective function, by the maximization for seeking its difference Guarantee low sidelobe, then constrained using bound pair main lobe under the main lobe upper bound and main lobe, increases the value in the main lobe upper bound, it is low in guarantee While secondary lobe, makes main lobe power as close as the main lobe upper bound, increases the difference of main lobe center power and peak side-lobe power, Low sidelobe characteristic is realized with this.Then left and right half-power beam point is utilized respectively as main lobe and secondary lobe watershed area, to guarantee Radar range applies equated constraint to covariance matrix diagonal entry, and finally to specific direction, there are the influences of strong clutter Null is generated to be inhibited.

Third step establishes semi definite programming problem using the above objective function and constraint condition, using convex in Matlab Optimization Toolbox is solved, and transmitting signal covariance matrix is obtained, and thus acquires transmitting signal power directional diagram.

4th step evaluates the validity of proposed low sidelobe method, is verified by the peak side-lobe comparison of transmitting pattern Low sidelobe characteristic verifies DOA by comparison spectral peak figure and estimates performance, passes through mean square error and Riming time of algorithm verification algorithm It can superiority and inferiority.Mean square error formula:

In formula, i indicate i-th Simulation results, α andIndicate corresponding pitch angle and azimuth input value, α_iWithPoint Not Biao Shi i-th simulation result output pitch angle and azimuth estimated value.

Feature of the invention is as follows:

(1) it is objective function using the maximum value of the difference of main lobe center power and peak side-lobe power, obtains preferable low Sidelobe performance.

(2) apply constraint using bound pair main lobe under the main lobe upper bound and main lobe, while increasing the main lobe upper bound, so that main lobe Center power increases the difference of main lobe center power and peak side-lobe power as close as the main lobe upper bound, is realized with this Low sidelobe characteristic.

(3) for the interference that may somewhere have strong clutter in space, null can be formed and inhibited, improved anti-dry Immunity energy.

Compared with prior art, the invention has the following advantages:

The invention proposes one kind to be based on MIMO radar low sidelobe direction of the launch drawing method, and with experiment simulation to algorithm Performance when sidelobe performance and progress DOA estimation is verified, and this method has more excellent peak compared with existing low sidelobe algorithm It is worth secondary lobe, and computational complexity and root-mean-square error are also smaller, root-mean-square error is to the especially big or special small error in one group of measurement Reflect it is very sensitive, so, root-mean-square error can be well reflected out the precision measured, i.e., expression DOA estimation effect more It is good.To improve MIMO radar low sidelobe characteristic and DOA estimation effect.

Detailed description of the invention

Fig. 1 MIMO radar low sidelobe transmitting pattern method system block diagram

Fig. 2 emission array model

Fig. 3 method and thought schematic diagram

Tetra- kinds of algorithm transmitting patterns of Fig. 4 compare, a) represent be four kinds of algorithm Direction Pattern Simulations as a result, b) represent its A) enlarged drawing in figure at the first peak side-lobe of the left side

When tetra- kinds of algorithm signal-to-noise ratio of Fig. 5 are 10dB, DOA estimation simulation result spectral peak comparison is carried out.Wherein scheme left side table in a Show Chebyshev's weighting algorithm spectrum peak search as a result, the right corresponds to contour map for it；Scheming the left side in b indicates association-integral secondary lobe Algorithm spectrum peak search is as a result, the right corresponds to contour map for it；Scheming the left side in c indicates association-peak side-lobe algorithm spectrum peak search knot Fruit, the right correspond to contour map for it；Scheming the left side in d indicates mentioned method spectrum peak search herein as a result, the right corresponds to for it etc. High line chart

Tetra- kinds of algorithms of Fig. 6 carry out mean square error root when DOA estimation and compare

Specific embodiment

Yi Xiajiehejutishishili,Bing Canzhaofutu,Dui Benfamingjinyibuxiangxishuoming.

Step 1 emulates MIMO radar transmitting signal, and radar mockup is set as what transmitting terminal was made of M array element Even linear array.Wherein a antenna element transmitting signal of m (1≤m≤M) is represented by s_m, then transmitting signal matrix can be indicated Are as follows:

S=[s₁,s₂,…,s_M]^T

Assuming that far field objects be located at intended recipient at θ to signal X be

X=a^H(θ)S

Wherein a (θ) indicates that MIMO radar emits signal guide vector, a^H(θ) is the transposition of steering vector a (θ),Carrier frequency is f_c, c represents the light velocity, and array element spacing is d.By This can obtain directional diagram expression formula P (θ) are as follows:

Wherein, L indicates that Baud Length, covariance matrix R are P (θ), and covariance matrix R will be straight as can be seen from the above equation Connecing influences transmitting pattern spatial characteristics, and P (θ) directly indicates distribution of the power at corresponding angle θ, obtains transmitting signal Model.

Step 2 utilizes Ω_SIndicate secondary lobe region, Ω_mMain lobe region is indicated, with θ₁, θ₂Respectively indicate the left half-power of main lobe Beam spot and right half-power beam point, centre folded by region be main lobe Ω_m, the region other than left and right half-power beam point is Ω_S。 Transmitting pattern θ can be obtained_s(θ_s∈Ω_s) direction side-lobes power expression formula are as follows:

a^H(θ_s)Ra(θ_s),θ_s∈Ω_s

Transmitting pattern θ_m(θ_m∈Ω_m) direction main lobe power expression:

a^H(θ_m)Ra(θ_m),θ_m∈Ω_m

Step 3 lacks due to minimizing secondary lobe algorithm and integral secondary lobe algorithm to constraint of the main lobe, is easy to produce main lobe distortion The problems such as, it is constrained using bound pair main lobe under the main lobe upper bound and main lobe, increases the value in the main lobe upper bound, guaranteeing the same of low sidelobe When, make main lobe power as close as the main lobe upper bound, increase the difference of main lobe center power and peak side-lobe power, is come with this real Existing low sidelobe characteristic.Set the main lobe upper bound as β and main lobe lower bound be η, η be set as herein 1, β indicate constraint of the main lobe be it is variable, Its constraint is as follows:

η indicates main lobe lower bound, then:

a^H(θ_m)Ra(θ_m)≥η,θ_m∈Ω_m

β is the constraint of the main lobe upper bound, is made:

|a^H(θ_m)Ra(θ_m)-η|≤β,θ_m∈Ω_m

Step 4, θ_m0(θ_m0∈Ω_m) indicate main lobe center power point, the constraint of three dB bandwidth half power points are as follows:

In step 5, actual environment, might have clutter in secondary lobe area, (radar scattering of other objects other than target is returned Wave) it influences to receive signal, cause the echo signal-to-noise ratio of MIMO radar to reduce, and then influence MIMO radar and estimate performance；It therefore can In secondary lobe region clutter θ_l(θ_l∈Ω_s) at generate corresponding null to inhibit to strong clutter.If (δ is any for δ > ε > 0 Number greater than 0), if there is the influence of clutter, can be added in constraint condition:

a^H(θ_l)Ra(θ_l)≤ε,θ_l∈Ω_s

Step 6 is to guarantee that each array element transmission power is equal, does not influence MIMO radar detection performance, enables R_mmIndicate the of R M (0 < m < M) a diagonal entry adds following constraint:

R_mm=1/M

Step 7, using the difference of main lobe center power and peak side-lobe power as objective function, guarantee its low sidelobe characteristic, θ_m0(θ_m0∈Ω_m) indicating main lobe central point, objective function form is as follows:

a^H(θ_m0)Ra(θ_m0)-a^H(θ_s)Ra(θ_s)

Step 8 enables covariance matrix R >=0 guarantee its Positive, utilizes the constraint function and step 3, step in step 7 Rapid 4, step 5, the constraint condition of step 6 establish positive semidefinite Optimized model as follows:

Step 9 obtains Optimized model by step 8, is solved, is obtained using Matlab convexity Optimization Toolbox cvx Emit signal covariance matrix, and then acquires transmitting signal.

Step 10, evaluation and test low sidelobe characteristic, it is non-with Chebyshev's weighting algorithm, based on covariance using the mentioned method of this paper The modified minimum peak side-lobe algorithm of diagonal entry and minimum integral secondary lobe algorithm carry out emulation and obtain its direction of the launch Figure simulation result is as shown in a in Fig. 4, and wherein b is enlarged drawing at the first peak side-lobe in Fig. 4.Four kinds of algorithm peak side-lobe numerical value Such as table 1.(for convenience of describing, covariance amendment off diagonal element method is referred to as " association-")

1 four kinds of algorithm peak side-lobe data of table compare

Algorithm title	Chebyshev's weighting	Association-integral secondary lobe	Association-peak side-lobe	Context of methods
					Peak side-lobe	-16.03	-16.69	-17.46	-17.35

Step 11 is verifying four kinds of algorithms simulation performance when carrying out DOA estimation, utilizes hair obtained by the design of four kinds of algorithms Signal is penetrated, then carries out DOA estimation using 2D-MUSIC algorithm, gained spectral peak is as shown in Figure 5.

Step 12, the performance superiority and inferiority of tradeoff four kinds of algorithm DOA estimation

In the case where two conditions of emulation are constant above, signal-to-noise ratio is changed to SNR ∈ [- 10,10], the value of each signal-to-noise ratio Add 2.The joint root-mean-square error (RMSE) of angle estimation is to weigh the important criteria of the performance superiority and inferiority of DOA estimation, combines RMSE Is defined as:

Wherein, i indicate i-th Simulation results, α andIndicate corresponding pitch angle and azimuth input value, α_iWithPoint Not Biao Shi i-th simulation result output pitch angle and azimuth estimated value.Carry out 100 independences respectively under each signal-to-noise ratio It is as shown in Figure 6 with SNR transformation results to acquire root-mean-square error RMSE for emulation experiment.When record signal-to-noise ratio is 0dB, 10dB respectively It carries out 100 independent repetitions to test, record DOA estimation mean square error and average operating time such as table 2.(computer processor: Intel(R)Core(TM)2Quad CPU [email protected]；Memory: 4.5GB is installed；OS Type: 32)

The comparison of the mean square error and runing time of 2 algorithms of different of table

Present invention is characterized in that

1, it establishes based on MIMO radar low sidelobe transmitting pattern method model, with bound pair master under the main lobe upper bound and main lobe Valve is constrained, and while realizing to main lobe regulation, guarantees its low sidelobe characteristic.

2, it is objective function using the maximum value of the difference of main lobe power and peak side-lobe power, semi definite programming is established with this Problem realizes low sidelobe characteristic.

3, the problem of influencing for a direction in space there may be clutter, can form null in specific direction and be pressed down System.

Above embodiments are only exemplary embodiment of the present invention, are not used in the limitation present invention, protection scope of the present invention It is defined by the claims.Those skilled in the art can within the spirit and scope of the present invention make respectively the present invention Kind modification or equivalent replacement, this modification or equivalent replacement also should be regarded as being within the scope of the present invention.